N.Y. CPLR 1021
A motion for substitution may be made by the successors or representatives of a party or by any party. If a person who should be substituted does not appear voluntarily he may be made a party defendant. If the event requiring substitution occurs before final judgment and substitution is not made within a reasonable time, the action may be dismissed as to the party for whom substitution should have been made, however, such dismissal shall not be on the merits unless the court shall so indicate. If the event requiring substitution occurs after final judgment, substitution may be made in either the court from or to which an appeal could be or is taken, or the court of original instance, and if substitution is not made within four months after the event requiring substitution, the court to which the appeal is or could be taken may dismiss the appeal, impose conditions or prevent it from being taken. Whether or not it occurs before or after final judgment, if the event requiring substitution is the death of a party, and timely substitution has not been made, the court, before proceeding further, shall, on such notice as it may in its discretion direct, order the persons interested in the decedent's estate to show cause why the action or appeal should not be dismissed.
N.Y. CPLR 1021